Analog integrated circuits (ICs) are now being extensively used, for example, in wireless radio frequency (RF) applications such as cellular telephones where high frequencies are encountered. Many analog ICs include inductive elements, such as inductors, formed by a conductor. Inductive elements with a relatively high quality (Q) factor, or low loss, are preferably used in analog ICs. As a result, the analog integrated circuits have superior performance, including selectivity, noise figure, and efficiency. Relatively high Q inductors have been formed on insulating bulk semiconductors, such as gallium arsenide.
Most integrated circuits, however, are formed on silicon. In comparison to gallium arsenide ICs, silicon ICs can be fabricated relatively inexpensively. Also, analog and digital circuits may be readily combined on silicon ICs. However, unlike gallium arsenide, silicon is a conductive bulk semiconductor. As a result, conventional inductive elements formed on silicon are relatively lossy, and thus have relatively low Q factors. For example, Q factors of 3 to 8 are reported for inductors fabricated on silicon in Nguyen et al., "Si IC-compatible inductors and LC Passive Filters," IEEE Journal of Solid-State Circuits, vol. 25, no. 4, p. 1028-1031, 1990, herein incorporated by reference.
An inductor formed on an IC 101 may be a conventional rectangular spiral inductor 103, as illustrated in FIG. 1A. The conventional rectangular spiral inductor 103 includes substantially parallel conductive branches 121 that are mutually coupled to increase the rectangular spiral inductor's 103 effective inductance.
The conventional rectangular spiral inductor 103 is formed in the following manner. A first conductor 109 is patterned on the IC 101. Then, an insulator, such as resist, defining the location of air bridges 105, is patterned on the IC 101. Next, a second conductor 107 is patterned on the IC 101. However, where an air bridge 105 is to be formed, the insulator separates the first and second conductors 107, 109. Finally, conventional air bridges 105 are formed by removing the insulator.
Conventional air bridges 105, in this example, permit the two conductors 107, 109 to cross one another, without making electrical contact, as illustrated in FIG. 1B. Conventional air bridges 105 are formed by substantially perpendicular conductors 107, 109 to diminish undesired magnetic coupling between the conductors 107, 109. Further, relatively low-dielectric-constant air typically separates the conductors 107, 109 to diminish undesired capacitive coupling between the conductors 107, 109.
FIG. 1C illustrates a prior art first order lumped element electrical model of the rectangular spiral inductor 103 that describes the electrical characteristics of the rectangular spiral inductor 103 below its self-resonant frequency. The self resonant frequency is the maximum frequency at which the rectangular spiral inductor 103 acts as an inductor. Above the self resonant frequency, for example, the rectangular spiral inductor may exhibit capacitive characteristics.
L is the effective inductance of the rectangular spiral inductor 103. The effective inductance represents the sum of both self and mutual inductances of the branches 121. The inductance, L, of the rectangular spiral inductor 103 is determined by (1) the length of the branches 121, (2) the spacing between the branches 121, and (3) the number of branches 121, or turns.
The other model elements are parasitics that result from the physical implementation of the rectangular spiral inductor 103. R.sub.DC and R.sub.SKIN EFFECT are respectively the lumped element equivalent DC and skin effect resistances of the conductors 107, 109. R.sub.DC is determined by the cross-sectional area, length and resistivity of the conductors 107, 109. R.sub.SKIN EFFECT is determined by the thickness of the conductors 107, 109. C.sub.s is a lumped element equivalent capacitance representing the interwinding capacitances between the parallel conductive branches 121. C.sub.s is determined by both the distance between adjacent branches 121, and the dielectric constant of the material proximate to those adjacent branches 121. The C.sub.p s are lumped element equivalent capacitances representing capacitances between the conductors 107, 109 and a ground plane under the IC 101 on which the rectangular spiral inductor 103 is formed. The C.sub.p s correspond to the width of the conductors 107, 109, and the thickness and dielectric constant of the material between the conductors 107, 109 and the ground plane. R.sub.SUBSTRATE is a lumped element equivalent resistance corresponding to substrate losses. The Q factor and self-resonant frequency of the rectangular spiral inductor 103 are a function of the reactances and resistances described by the electrical model of FIG. 1C.
To increase its Q factor, resistances and/or capacitances of the rectangular spiral inductor 103 should be reduced. One technique for reducing the Q factor of the inductor is disclosed in J. N. Burghartz et al., "Integrated RF and Microwave Components in BiCMOS Technology," IEEE Trans. Electron Devices, vol. 43, no. 9, pp. 1559-1570, 1996 (herein after the "Burghartz Article"), herein incorporated by reference. The Burghartz Article discloses inductors, on silicon ICs, whose conductors are displaced above the silicon, and are encased in oxide. These inductors have Q factors exceeding 10. The higher Q factors arise, in part, because the inductors, disclosed in the Burghartz Article, have relatively lower values of C.sub.p because the conductors are farther displaced from the IC ground plane by the oxide.
Further, the inductors disclosed in the Burghartz Article require a complex five-level metal silicon technology that is more complicated than conventional two-to four-level metal silicon technologies. Therefore, there is a need for inductors having relatively high Q factors that can be formed with conventional silicon technologies.